#include <cmath>
#include "nr.h"
using namespace std;

void NR::tred2(Mat_IO_DP &a, Vec_O_DP &d, Vec_O_DP &e)
{
  int l,k,j,i;
  DP scale,hh,h,g,f;

  int n=d.size();
  for (i=n-1;i>0;i--) {
    l=i-1;
    h=scale=0.0;
    if (l > 0) {
      for (k=0;k<l+1;k++)
	scale += fabs(a[i][k]);
      if (scale == 0.0)
	e[i]=a[i][l];
      else {
	for (k=0;k<l+1;k++) {
	  a[i][k] /= scale;
	  h += a[i][k]*a[i][k];
	}
	f=a[i][l];
	g=(f >= 0.0 ? -sqrt(h) : sqrt(h));
	e[i]=scale*g;
	h -= f*g;
	a[i][l]=f-g;
	f=0.0;
	for (j=0;j<l+1;j++) {
	  // Next statement can be omitted if eigenvectors not wanted
	  a[j][i]=a[i][j]/h;
	  g=0.0;
	  for (k=0;k<j+1;k++)
	    g += a[j][k]*a[i][k];
	  for (k=j+1;k<l+1;k++)
	    g += a[k][j]*a[i][k];
	  e[j]=g/h;
	  f += e[j]*a[i][j];
	}
	hh=f/(h+h);
	for (j=0;j<l+1;j++) {
	  f=a[i][j];
	  e[j]=g=e[j]-hh*f;
	  for (k=0;k<j+1;k++)
	    a[j][k] -= (f*e[k]+g*a[i][k]);
	}
      }
    } else
      e[i]=a[i][l];
    d[i]=h;
  }
  // Next statement can be omitted if eigenvectors not wanted
  d[0]=0.0;
  e[0]=0.0;
  // Contents of this loop can be omitted if eigenvectors not
  //	wanted except for statement d[i]=a[i][i];
  for (i=0;i<n;i++) {
    l=i;
    if (d[i] != 0.0) {
      for (j=0;j<l;j++) {
	g=0.0;
	for (k=0;k<l;k++)
	  g += a[i][k]*a[k][j];
	for (k=0;k<l;k++)
	  a[k][j] -= g*a[k][i];
      }
    }
    d[i]=a[i][i];
    a[i][i]=1.0;
    for (j=0;j<l;j++) a[j][i]=a[i][j]=0.0;
  }
}
